TITLE: What's the difference between predicate and propositional logic?
QUESTION [128 upvotes]: I'd heard of propositional logic for years, but until I came across this question, I'd never heard of predicate logic.  Moreover, the fact that Introduction to Logic: Predicate Logic and Introduction to Logic: Propositional Logic (both by Howard Pospesel) are distinct books leads me to believe there are significant differences between the two fields.  What distinguishes predicate logic from propositional logic?

REPLY [5 votes]: I think this example from "Overview of proposition and predicate logic
" by Jan Kuper gives a suitable explanation.
In proposition logic, we can express statements as a whole, and combinations
of them. Intuitively, a statement is a sentence in which something is
told about some reality, and which can be true or false about that reality.
For example, if p is the statement ”Albert is at home”, and q means ”the
door is locked”, then q→¬p says: ”if the door is locked, then Albert is not
at home”.
In first-order predicate logic, a statement has a specific inner structure,
consisting of terms and predicates. Terms denote objects in some reality,
and predicates express properties of, or relations between those objects.
For example, the same example as before might be expressed as
Locked(d) → ¬AtHome(a). Here, Locked and AtHome are predicates,
and d and a are terms, all with obvious meanings.